Orbifold String Topology I

Date: 05/02/2007

Lecturer(s):

Bernardo Uribe (Universidad de los Andes)

Location:

University of British Columbia

Topic:

In these two lectures I will survey my recent work with Lupercio and
Xicotencatl on the properties of the homology of the free loop space of
an orbifold. In the first lecture I will review the work of Chas and
Sullivan on string topology and I will describe how this theory could
be generalized to the space of free loops on an orbifold. I will also
review the Hochschild version of string topology due to Cohen and Jones
and how this construction could also be generalized to the orbifold
case. At the end of the lecture I will show some simple examples to get
a flavor of the theory. In the second lecture I will show how the
orbifold string topology on the symmetric product gives rise to a ring
structure on the cohomology of the inertia orbifold; this we have
coined the virtual cohomology. Then I will explain the relation between
the virtual cohomology and the Chen-Ruan cohomology. To finish I will
show how to calculate in general the virtual cohomology, and I will
give some examples.